{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "134e7f9d",
   "metadata": {},
   "source": [
    "# API Demo 2: Plotting"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2571d531",
   "metadata": {},
   "source": [
    "### Initialize KAN and create dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "2075ef56",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(torch.Size([1000, 2]), torch.Size([1000, 1]))"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from kan import *\n",
    "# create a KAN: 2D inputs, 1D output, and 5 hidden neurons. cubic spline (k=3), 5 grid intervals (grid=5).\n",
    "model = KAN(width=[2,5,1], grid=5, k=3, seed=0)\n",
    "\n",
    "# create dataset f(x,y) = exp(sin(pi*x)+y^2)\n",
    "f = lambda x: torch.exp(torch.sin(torch.pi*x[:,[0]]) + x[:,[1]]**2)\n",
    "dataset = create_dataset(f, n_var=2)\n",
    "dataset['train_input'].shape, dataset['train_label'].shape"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8c6add1d",
   "metadata": {},
   "source": [
    "### Plot KAN at initialization"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "ac76f858",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 500x400 with 16 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot KAN at initialization\n",
    "model(dataset['train_input']);\n",
    "model.plot(beta=100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "ee036e1e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 500x400 with 16 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# if you want to add variable names and title\n",
    "model.plot(beta=100, in_vars=[r'$\\alpha$', 'x'], out_vars=['y'], title = 'My KAN')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ddf67e30",
   "metadata": {},
   "source": [
    "### Train KAN with sparsity regularization"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "97111d75",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "train loss: 1.57e-01 | test loss: 1.31e-01 | reg: 2.06e+01 : 100%|██| 20/20 [00:11<00:00,  1.80it/s]\n"
     ]
    }
   ],
   "source": [
    "# train the model\n",
    "model.train(dataset, opt=\"LBFGS\", steps=20, lamb=0.01, lamb_entropy=10.);"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2f30c3ab",
   "metadata": {},
   "source": [
    "### $\\beta$ controls the transparency of activations. Larger $\\beta$ => more activation functions show up. We usually want to set a proper beta such that only important connections are visually significant. transparency is set to be ${\\rm tanh}(\\beta |\\phi|_1)$ where $|\\phi|_1$ is the l1 norm of the activation function. By default $\\beta=3$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "3f95fcdd",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 500x400 with 16 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model.plot(beta=3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "6383a22f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 500x400 with 16 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model.plot(beta=100000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "9f6ff7e1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 500x400 with 16 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model.plot(beta=0.1)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "61d537b7",
   "metadata": {},
   "source": [
    "### After purning, \"mask=True\" will remove all connections that are connected to unsignificant neurons. The insignificant neurons themselves are still visualized. If you want those neurons to be removed as well, see below. Insignificant/Significant neurons are defined based on l1 norm of its incoming and outgoing functions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "1269a698",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 500x400 with 16 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model.prune()\n",
    "model.plot(mask=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "2249bb17",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 500x400 with 16 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model.plot(mask=True, beta=100000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "1e5b8732",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 500x400 with 16 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model.plot(mask=True, beta=0.1)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9e788b91",
   "metadata": {},
   "source": [
    "### Remove insignificant neurons"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "ed4800ea",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 500x400 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model2 = model.prune()\n",
    "model2(dataset['train_input']) # it's important to do a forward first to collect activations\n",
    "model2.plot()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "61c8eeb1",
   "metadata": {},
   "source": [
    "### Resize the figure using the \"scale\" parameter. By default: 0.5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "5cb8d57e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 500x400 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model2.plot(scale=0.5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "67305f39",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 200x160 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model2.plot(scale=0.2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "51c722ad",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 2000x1600 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model2.plot(scale=2.0)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "03d4bf1b",
   "metadata": {},
   "source": [
    "### If you want to see sample distribution in addition to the line, set \"sample=True\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "c6d24148",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 500x400 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model2(dataset['train_input'])\n",
    "model2.plot(sample=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a3fa482a",
   "metadata": {},
   "source": [
    "### The samples are more visible if we use a smaller number of samples"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "3856bcb6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 500x400 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model2(dataset['train_input'][:20])\n",
    "model2.plot(sample=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4fa7ca2c",
   "metadata": {},
   "source": [
    "### If a function is set to be symbolic, it becomes red"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "3d502880",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Best value at boundary.\n",
      "r2 is 0.9926980535347188\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "tensor(0.9927)"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model2.fix_symbolic(0,1,0,'x^2')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "f8f93b9c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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tOTk5WL58OZYtW4bU1FTzOkhkUQwXoouoqqrCgw8+CI/HAwAhoxVFUQAADocD69atQ0VFhSl9JLIqhgvRAKqqqrBw4UIIIaCq6kU/zmazQVEUVFZWMmCI+mG4EF3A5XJh/Pjx8Hq9lwwWjc1mQ2JiIpqbmzlFRtSHC/pEF1i1ahU8Hs+gggUAVFWFx+PB6tWrh7hnROGDIxeifoQQyMvLw+HDh69oR5iiKMjOzkZTU5O+HkMUzRguRP2cO3cOI0eOHPB9PwCwBUA8gK8AeC7y+RkZGUPWP6JwEWN2B4ispL29fcB2OwABYByAxwBkAjgKoAFAY9/beQBut5vhQgSGC0W57u5u7Nq1C9u3b0d1dTVqa2sH/LgAgD/2/e8GAIV9bzMA3NvX3gJg5JtvAjNnAoWFwMiRAKfIKEpxWoyiSkdHB3bs2IGamhpUV1dj9+7d6O3tRUpKCmbOnInS0lL87ne/Q0tLy6D/zDTIoLk9MxO/WboUyrFj8h2ZmcDUqTJopk4Fxo9n2FDU4MiFIlprayuqq6v1t4aGBqiqilGjRqGsrAz3338/SktLUVBQAJtNbp5UVRXPPPPMoBf02wF8pihY8txzUJ5+GnC7gf37gYYGoLER+PRTQFWBESNkyGhvWVmA3T6E/3oi83DkQhGlubkZNTU1+jRXU1MTAGDSpEkoLS3V37Kysi66q8vwcy7d3cCBAzJoGhuBgweB3l4gMREoKAiObvLygNjYa/nnE1kGw4XClhAChw4dQnV1NbZv346amhqcOHECADBlyhSUlpairKwMs2bNwtixY6/oz77SE/offPABysvLB/eH+3zAV1/JoGloAPbtA7xeGSxTpgRHNvn5MoCIwhDDhcJGIBDAvn37Qqa5zp07B5vNhhtvvFEflcycOdOQHVuDrS22fv36wQfLQFQVOHo0OI3W2AicPw/YbEBOTnBkc8MNgNN5Lf8komHDcCHL6u3txRdffKEHSW1tLdxuN+Li4nDzzTejrKwMpaWlKC4uRnJy8pD0weVyYfXq1XjxxRe/URX56aefxrJly5CSkmLsXyoE0NISHNU0NABnz8r3TZwY3CAwdSrAbc9kUQwXsgyPx4OdO3fq01w7d+5ET08PkpKSUFJSok9zTZ8+HfHx8cPat/73uTidTqSnpw/vSfwzZ4KjmoYGGT4AcN11waApLJSvuSONLIDhQqZxuVyora3VRyZ79uyB3+9Heno6Zs2ahVmzZqGsrAyFhYWIieHGxhAuV3BU09gIHDkiRzzp6XL6TBvdTJrEsCFTMFxo2Jw+fVoPkpqaGuzbtw9CCIwZMyZk8f3666/XtwXTIHV1ye3P2uimqQnw+4HkZBk22ugmJwdgUNMwYLjQkBBC4Pjx43qYbN++HUeOHAEAZGdn60FSWlqKiRMnstij0Xp6gC+/DE6jHTgg2+Lj5S40bWQzZQoQF2d2bykCMVzIEKqq4ssvvwzZyXXq1CkoioIbbrhB38k1a9YsjB492uzuRh+/Hzh0KHQqratLjmLy8oIjm4ICICnJ7N5SBGC40FXx+/1oaGgIqcnV1taGmJgY3HTTTfp6SUlJCS/QsiIhgGPHgiObxkagvV2uz2RlhZatMXo3HEUFhgsNSk9PD3bt2qWPSnbs2IGuri7Ex8ejuLhYH5nMmDEDDofD7O7SlRIC+Prr0LM2X38t3zduXOj251GjzO0rhQWGCw2os7MTO3bs0MNk165d6O3txYgRI1BSUqKfMZk2bRriOGcfmc6dk9No2ujm+HHZPnJk8FBnYaEMH66Z0QUYLgRAFnisqanR63LV19dDVVVkZmbqi+9lZWUoKCiAncUWo5PbHbpmc+iQrC6QkvLNgpzc7Rf1GC5RqqWlRQ+SmpoaHDx4EAAwYcKEkAKPOTk53MlFA/N65S40rZLAwYOybprDEVqQMzeXBTmjEMMlCgghcPjw4ZCdXMf7pjiuv/56fVQya9YsjB8/3uTeUtjq7ZXna7Q1m337ZEXouDjg+uuD6zb5+UBCgtm9pSHGcIlAgUAABw4c0Ecl27dvx9mzZ2Gz2VBYWKgHyaxZs5CZmWl2dylSBQKyckD/HWlut5wyy80NTqOxIGdEYrhEgN7eXuzZs0cPktraWnR0dCAuLg7Tp0/Xp7hKSkrg5ENMZhECaG4ODZtz5+T7Jk8OLVuTnm5qV+naMVzCkNfr1Qs8VldXo66uDt3d3XA4HCgpKdGnuW6++WYkcPqBrEoIWe25oSEYNidPyveNGRO6SYAFOcMOwyVMbNy4Edu2bUN1dTW++OIL+P1+pKam6iVUSktLUVRUhFgunFI4a28Prtk0Nsp7brSCnNoGgZkzedVAGGC4hInz589DVVXExMQgNjYWMTExsNvt3MlFkc3vBzo75VqN2y1L1uTlAaz6YHkMlzChqioURWGYUHQLBOT0GM/RWB7DhYiIDMf4JyIiw/HWoD6BQAB1dXVwu91mdyXsTZs2DaNY3DAsBQIBNB84gIDXa3ZXwl5mTg5GpKWZ3Q3TcFqsj9frxcKFC9Hd3Y3k5GSzuxOWtEoAK1euxIIFC8zuDl2Fnp4e1P/yl/D19sKWmGh2d8KSEAKxJ08i7ZlnkD1zptndMQ1HLn2EELDZbPjtb3+LW2+91ezuDLlAIIDe3l7Y7XbDqhr7fD488sgj4O8rYUwI+BUFo7/3PUwoKjK7N+Gho0Oe1xkzBkhMhD8QwN5f/zrqnwOGywViYmIQHx9vdjcMIYRAT08POjo6cPbsWZw4cQJHjhzBV199haNHj+LkyZPIyMjAs88+i7lz517zvfXczRY57HY7z0wNhhDArl3Ayy/Lqwjy84H77+dzAIZLxFJVFe+99x5eeuklNDc3w+12o6enB6qqhnxcU1MTfvjDH+Ktt97CTTfdxIeC6EoIAezdK4t2trQAbW3AokVm98oSuFssAgkhsHHjRvzsZz/Drl27cObMGXi93m8Ei6a1tRUrVqxAb2/vMPeUKMx1dQFffhl8PXasLFVDDJdII4TAnj178Itf/AIul+sb77fb7UhKSsL48eND7rbfuHEjtm7dGvXzxERXpLk5WHwTkMU3I2Ra/VpxWiyCCCFw4sQJPPPMM2hubtbb8/PzMW/ePOTk5CArKwvjxo1DRkYGPvzwQzz77LPw+/3o7u7Giy++iLKyMu6WI0kIedPkmTOyBEtuLotH9ieErH+mjfhtNoCbIHQMlwghhEB7ezt+/vOfo76+Xm/Pzc3F//7v/yI3NxcAQtZU7rvvPrz99tvYtm0bAGDnzp1477338K1vfYtrL9FOVYHdu4GNG4E9e4DRo4Hnnwe4PTkoEAD6PWtwOoGcHPP6YzGcFosQPp8Pzz//PDZv3qy3jRo1Cv/xH/+B3NzcAXdyJSUl4R/+4R+Q2PcDw+/346WXXsLZs2eHte9kUZs2AZ9+KrfaHj0qb5nktGnQ+fPyMjTN5MlAFB+avBDDJQIIIbBp0ya8/fbb+ppJUlISfvvb36K0tPSioxBFUXDbbbehoqJCbzt48CBef/31iy7+U5Sw2YDZswG7Xb72+YC//Y3hohECOHRIBoymsBCI4WSQhuESAc6ePYvf/e536O7uBiDP6vzsZz/D4sWLLzu9FRsbi5/85Cf64r4QAq+++iqOHj3Kxf1oN3Wq3P2k+fxzed8KSfX1cvoQkKFSWMg1qX4YLmFOVVX86U9/QmNjo942Z84cPPXUU7Brv3VegqIoKCoqwkMPPaS3nTp1Cn/60584eol2ycnArFnB162tch2Gv3QAPT3Avn3B15mZwIQJ5vXHghguYUwIgYMHD+Ivf/mLPspIS0vDr371KyQlJQ36z7Hb7fj+97+Psf1+S127di3q6+s5eolmigLcemtwEV8IYOtWeYFXtDt7Vm5D1uTmyjAmHcMljAUCAbz88ss417fPXlEUPPnkk5g2bdoV7/aaNGkSvvOd7+if53K58Pvf/54HK6PdxInAlCnB1wcPAsePm9cfKxBCfh20ytGKAtx4Iy8wuwC/GmFKCIHPP/8cf/3rX/W2yZMn46mnnrqqGmE2mw2PPfYYpvT7QfLRRx/h008/5eglmsXEALffHlxL8HqBbduie2pMCLneon0N4uNlTTGut4RguISp3t5e/OEPf0BnZycAGQ5///d/jzFjxlz1GZXMzEz8+Mc/Rkzfjhev14sXX3wRXV1dhvWbwoyiANOnAxkZwbaaGnmoMlp5PHLkomHJlwExXMKQEAJ1dXXYunWr3lZYWIiHHnromg4/KoqCe++9FyUlJXrbjh078P7773P0Es3S0oBbbgm+PnlSLmZH6/dEc7Ncc9Hk5wMJCeb1x6IYLmHI7/fjz3/+MzweDwC5IP+DH/wgpFbY1UpKSsLTTz+NhL6Hxe/3Y+XKlfq6DkUhRZFnXrQS/IGAPFwZjbsJhZDBqq1Faust9A0MlzAjhEBDQwM2bdqkt91www1YsGCBISVbFEXB7Nmzcdddd+ltBw4cwBtvvMHRS7RSFOD664FJk4Jt+/bJk/vR5sKSLyNGsObaRTBcwoyqqli9ejXcbjcAudbyxBNPYMSIEYb9HXFxcVi+fDlSUlIABA9WHjt2jAETrRIS5NqLpq0N+Oqr6JsaO38eOHw4+HriRCA93bz+WBjDJYwIIdDU1ITKykq9LTs7G4sWLTK00KSiKJg2bRqWLFmit7W0tPBgZTTTFva18iaBgDxQGU2EkLXE+pd8KSpiyZeLYLiEESEEXn/9dbS1tQGQIfDoo48iMzPT8L/LZrPh+9//PsaMGaO3rVmzBg0NDRy9RKvJk+VVvprGRqCv5FDUaGiQwQrIUJk61dz+WBjDJYwcP34c69ev11+PGzcODz744JCUx1cUBVlZWXjqqaf0P7+9vR1/+MMf4PP5DP/7KAwkJQEFBcHXJ0/Kt2jR2yvDRZOeLtehuN4yIIZLmBBCYM2aNTh9+rTe9vDDD4eMLIxms9nw7W9/G3l5eXrbhg0b8Nlnn3H0Eo0UBZg2LfjDtLs7urYks+TLFWG4hInW1lasW7dOfz1q1CgsXbr0qk7jX4mRI0fiRz/6EQ9WkgyV/Hw5gtH0rwwcyYQAvvxSHqDUsOTLJfErEwaEENiyZQuOHj2qty1cuBBZWVlD/ncrioLFixdjxowZelttbS02btzI0Us0ysgAxo8Pvj50KDpO6wsB7N0bHKUlJMgpQk6JXRTDJQz09vbi7bffRqBvIdHhcODhhx8etquIk5OTsXz5csTHxwOQt17+z//8j36Ik6JIXBxwww3B121t0VHI0uuVIxfNddex5MtlMFwsTgiBxsZG7NixQ2+75ZZbUFRUNGzhoigK5syZg7KyMr3t888/x9atWzl6iUaFhcHpIL8/OtZdWlqAfuudKChgyZfLYLhYnBACa9eu1dc4bDYbli5dqo8ihktCQgK++93vIi4uDoAcTb3yyiv67ZcUJRQFyMoC+g7YApA7qCL5jpeBSr4UFXFK7DIYLhZ3+vRpfPjhh/rrSZMm4Y477hi2UYtGKwtTXFyst9XW1mL79u0cvUSb1NTQUjDHjgEul1m9GXqqGlryxekE8vIYLpfBcLEwIQQ++ugjtLS06G2LFi3CyP4H2YaRw+HA9773PcT2FTDs6enBK6+8gp6eHlP6Qyax2+XUmOb8eXlyPVJ/yRio5Ev/KwhoQAwXC/N6vVizZo0+MnA6nXjggQdM64+iKJg3bx6m96sx9dlnn6Guro6jl2iiKHJRXyt7oqqhhwsjiRDA0aNAe3uwbepUlnwZBIaLRQkhsGvXLuzZs0dvKysrw5QpU4Z9Sqy/pKQkfPe73w059/LKK6/w1H60ufC39/5rEpGmvj5Y8sVul+stdFkMF4tSVRVr1qzRF8xjYmLwyCOP6FNSZlEUBXfddRcK+02LfPLJJ9i1a5eJvaJhl5wM5OQEX7e0AK2t5vVnqPh8soaahiVfBo3hYlEnTpzAxo0b9de5ubmYPXu2qaMWjdPpxFNPPQW73Q4A8Hg8ePXVVzl6iSY2W+hv8F1dQFNT5K27nDsHnDgRfJ2bKxf06bIYLhYkhEBlZSXO9rtK9f7779fvVzGboii45557kJ+fr7d9/PHHaIjUeXf6Jq0UjLYlXojIW3cRAtizRwanpqiIJV8GiV8lC+rs7MS6dev0RfKMjAwsXrzYEqMWTWpqKp588knYbDbY7Xbk5OSgN1Ln3GlgY8YAo0YFXx88KE+yR4qeHmDz5uBozOGQu+Qs9BxaGbc8WIwQAtXV1di/f7/eNnfuXEyePNm8Tg1AURTce++9qK6uRkVFBcrLy4f9YCeZLDFRnvfQpo1aWmQpmClTwv8HsBDAgQOydpqmqCi0rhpdEsPFYgKBAN5++219/SIuLg5Lly7V1zesJCMjAy+99BLsdjsUReHIJdooClBcDGzZIrcj9/YCO3bIcAl3qgps2iQX9AG5S+zOO7kF+QpwWsxiDh06hL/97W/666lTp6KkpMRSU2IaRVEQExNjyb7RMFAUeeaj/5bknTsjY2rs5Emg/w7ISZNkiX1+rw8aw8VChBB499130d53YEtRFCxZsgRJ/e/PILKSlJTQXWPNzXIqKZx3jQkBfPYZ0NEhXysKcPvtcs2FBo3hYiHt7e1499139dejR4/GPffcw5EBWZeiAGVlctoIkNNItbXm9ulaud1Av9kDpKbKfyOfwyvCcLEIIQS2bt2Kw/1qGJWXl2Ps2LEm9oroMrQtyf3r3e3aFbp9N5wIAezeLafFNCUlof8+GhSGi0X09vZizZo1+oVgiYmJePjhh4f8GmOia+Z0AjfdFHx96lT4Hqj0+YCNG4NXN8fHA3fcwbMtV4FfMQsQQmD//v2orq7W26ZPn45p06ZxSoysT1GA0tLg1JjfD9TUhF+4CCGrHx84EGzLz5en8vkcXjGGiwUIIbBu3Tp09t1FbrPZ8PDDDyOBN91ROFAUed6l/7W/u3fLtYtwIoQ8NKldgGezye3HJtfzC1cMFws4c+YMKisr9dcTJkzA/PnzOWqh8JGcDNx8c/D1mTPyxH44jV7OnQvdjDBmjPw38Tm8KgwXkwkh8PHHH6O5uVlvu+eeezCqf1kNonAwa1bwt/xAILymxoQAqqtD72257TZgxAjz+hTmGC4m0y4EU/sWEJ1OJ5YsWcKFfAoviiJL8Pff3bhnj7zFMRx4vcAnnwTD0OkE5szhqOUa8CeYibQLwXbv3q23lZaWoqCgwMReEV0lhwOYMSP4+tw5eYmY1UcvWkXno0eDbdOnA+PGmdalSMBwMZFVLwQjuiqKIs+ExMXJ16oqp8a0bb1WFQjI7cfabZMxMXIhn7MH14RfPRMdP378GxeCzZkzhwv5FL6ysuQVyJr6esDlMq07g3LihJzC02RnAwUFnBK7RgwXkwgh8N577+HMmTN62wMPPGCZC8GIrkpCgqyUrGlrkwFj1akxVZVVnT0e+VpR5KFJHgO4ZgwXk7hcLqxdu1Z/nZmZabkLwYiumFaGX/vhLIS1p8bOnwe2bQu+zsyUu974HF4zhosJhBDYvHkzmpqa9Lby8nLLXQhGdFUmTJAl6jWNjXJx32qEkPfP9Js9QGkpkJZmXp8iCMPFBN3d3Xjttdf0OmIOhwPf+ta3uP2YIkN8PDBzZvD1+fPA3r3Wmxrr6QndfpyYCMybx1GLQfjTbJgJIVBTU4O6ujq9rbi4GNOnT+eUGEUGRZFbkhMT5WvtgKK2G8sKhJAVBPrNHqCwUI64+BwaguEyzHw+H1599VV9+3FsbCyWLVvG++cpsowbJw9Vag4cCJ1+Mpuqyjpi2tXcvMbYcAyXYSSEwJ49e0KuMS4qKsK8efM4aqHIEhsbOjXW2Ql88YV1psZOnwY+/zz4evx4YNo0jloMxHAZRoFAAKtWrUJX30VKNpsNy5YtQ3Jyssk9IzKYogC33AJoV3Rru8b8fnP7pfXl00+DpWkUBZg7N9hXMgTDZZgIIXDw4EFs2LBBb8vLy8Pdd9/NUQtFpuuuk6X4NU1NwNdfm9cfTWdn6DXGKSnArbdy1GIwhsswUVUVr732Glx9p5UVRcFjjz2GNG57pEgVExN6ZqSzU05FmTk1JoScnmtpCbYVFwOsQm44hsswEEJg3759WLdund42ceJE3H///Ry1UORSFFkAsv+0b22tvErYLH5/aB2xuDjWERsi/IoOg97eXrz44otoa2sDIEctS5cuxXX9b+4jikSjRsmrgjWHDoWOGoaTdo3xvn3BtilTeI3xEGG4DDEhBLZu3Rqy1pKbm4snnniCoxaKfHa7PPWufa97vcDOneZMjQkhD01q1xhrdcS0Ks5kKIbLEHO73fjP//xPeL1eALKs/vLlyzF69GiTe0Y0DBQFuPFGuWiu2bFDno4fbufOyR1rmjFj5GFP/pI3JBguQ0gIgbVr12LXrl1626xZs3Dfffdx1ELRIzMTuOGG4OujR2WZ++GkbYXum5oGIHeIsQr5kGG4DBEhBJqbm/Ff//VfITXEnn32WSRxPz1FE5stdGqsu1uOXoZzauzCa4yTk4Hbbx++vz8KMVyGiKqq+OMf/4ij/a5OXbx4MUpLSzlqoeiiKEBREZCeHmzbtEku7A9HwAghKzP3v8Z42jR5Kp/P4pBhuAwBIQT27t2LN998U28bNWoUli9fjhjWLqJolJoK3Hxz8PXZs8Dq1cOz9hIIyDDTqgPExADz53P78RDjV9dgQgi0tbXh+eefDzkw+Z3vfAe5ubkctVB0stmAJUvkqX3Njh1AZeXQlYQRQhao/PJLeXBSk5Ul14D4LA4phstFBAIBNDQ06Lu8BkMLlmeeeQZbt27V2/Pz87Fs2TLe10LRS1Hk7qzHHpNFLQE5onjjDeCDD4wvx6+qsjjln/8M/Ou/An31/KAo8s4W7ToAGjL8aTeA7u5uvPzyy3jggQfwyiuv6AvylyKEQGtrK37605/iww8/hOibS3Y4HPjlL3+JzMzMoe42kbUpityh1f9Crt5eYNUq4wJGCDnl9sYbwC9/CbzzTrBAJcBrjIcRFwAu0N3djeeeew6vvfYafD4f/v3f/x2jRo3CkiVLYLfbB/wcLVieeeYZbNiwISRYnnvuOSxYsIDTYUSAXO948klZZ6y6WoaBFjAdHcBdd8kAUJTBB4AQMpjOnAG2bQM2bBj47pjMTODxx4GMDEP/STQwhssF7HY7hBDw980Dd3Z24le/+hVsNhsWLVqE2NhY2Gy2kLDQRixVVVUhwfLP//zPePLJJ7mIT6RRFLkN+Mc/Dp49EUIu7L/1FlBVJUcW8+fLtZGYmIFDRguU1la5nlJdLW+W7Oz85sempck/b8ECYORIjlqGCX/qXSA2Nhb/9E//hOPHj2Pz5s0A5Cn7f/zHf8RLL72ElJQUpKenIz09HZmZmUhLS8OmTZvwySefhATLv/zLv2DZsmUMFqILKQrgdAYDprY2uCW5vR348EN5JuWGG4DbbgMcjtDP9/mA48eB/fvlf93ugbc0jxgh72lZuFBuJOCa57DiT74BpKWlYcWKFfjRj36ETz/9FADg8XhQX19/2c9lsBANgqLIH/4/+YkcWXz6aeioo7sb2LVLvl040rjc2ZjkZLm2c++9wIQJVzbFRobhT78BKIqC6667DitXrsQPf/hDbNu2bVCf53A48Otf/xpPPPEEg4XocrSA+cEPZBBs2SIv8Tp9OjRABnPQMiEByMmRU2ozZsidaTYbQ8VE/Al4EYqiYMyYMfjv//5vrFy5Eo2NjXC5XHC73ejq6oLX60Vvby/8fj9UVYXT6cRzzz2Hxx9/nMFCNFiKIisnT5gAfPvbMmTq6oCPPwa++uriZ2BsNhlMkybJwpgzZsgT9xdbo6Fhx5+Cl6AoCkaPHo3f/OY3CAQC8Pv98Pl88Hq98Hg8cLvdOH/+PDo6OjBu3DgUFhZedEcZEV2GosiT/PPnA7NnA0eOyErGA31cerocnTidMpwYKJbDcOlHVVXU1dXB4/Fc0efZbDacOnUKp06dGqKehQe/34/29nazu0HXyCYEzhw4AL9274mZLnbXitst3ywoEAgg4HYj2uOO4dLHZrMhPz8fGzduxMaNG83uTthyOp1IYRnzsGWz2YCJEyF27kTrzp1mdydsxTocsPe/3jkKKUIMZ91r69LOtvDLce1iYmJY6iZMCSEQCAT4HBjAbrdH9XPAcCEiIsNFb6wSEdGQYbgQEZHhGC5ERGQ4hgsRERmO4RImuJuNCLIScleX8ZeLkeEYLmGivr4e11133aCKZxJFrKNHgUcekf8lS2O4EBGR4RguRERkOIYLEREZjuFCRESGY7gQEZHhGC5ERGQ4hgsRERmO4UJERIZjuBARkeEYLkREZDiGCxERGY7hQkREhmO4EBGR4RguRERkOIZLGBBCoL29Haqqor29nXe6UFQSQqCtrQ0ejwdtbW18DiyO4WJhLpcLK1asQF5eHubOnYv29nbMnTsXeXl5WLFiBVwul9ldJBpy/Z+D4pISbNq8GcUlJXwOLE4RjH9LqqqqwoMPPgiPxwMAIb+lKYoCAHA4HFi3bh0qKipM6SPRULvwOcgSAi8A+CmAI3wOLI0jFwuqqqrCwoUL4fV6IYT4xvBfa/N6vVi4cCGqqqpM6inR0OFzEN44crEYl8uF8ePHw+v1QlXVy368zWZDYmIimpubkZqaOvQdJBoGF3sOsgF95HK438fzObAejlwsZtWqVfB4PIMKFgBQVRUejwerV68e4p4RDR8+B+GPIxcLEUIgLy8Phw8fvqKdMIqiIDs7G01NTfp6DFG4utRzcLGRC8DnwGo4crGQ1tZWHDp06Iq3WAohcOjQIbS1tQ1Rz4iGD5+DyMBwsZDOzs5r+ny3221QT4jMw+cgMjBcLCQ5OfmaPt/pdBrUEyLzXOo5aIacEmu+xOfzObAGhouFZGRkICcn54rnixVFQU5ODtLT04eoZ0TD51LPQS/kWkvvAJ/H58BaGC4WoigKli9fflWf+/TTT3MRkyICn4PIwN1iFsNzLkR8DiIBRy4Wk5qainXr1kFRFNhsl/6/x2azQVEUrF+/ng8URRQ+B+GP4WJBFRUVqKysRGJiIhRF+cYwX2tLTEzEBx98gPLycpN6SjR0+ByEN4aLRVVUVKC5uRkvvPACsrOzQ96XnZ2NF154AS0tLXygKKLxOQhfXHMJA9o9Fm63G06nE+np6Vy0pKjD5yC8MFyIiMhwnBYjIiLDMVyIiMhwDBciIjIcw4WIiAzHcCEiIsMxXIiIyHAMFyIiMhzDhYiIDMdwISIiwzFciIjIcAwXIiIyHMOFiIgMx3AhIiLDMVyIiMhw/w+V7VyIoR4QAwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 500x400 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model2.plot()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e75a0760",
   "metadata": {},
   "source": [
    "### If a function is set to be both symbolic and numeric (its output is the addition of symbolic and spline), then it shows up in purple"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "17df5fed",
   "metadata": {},
   "outputs": [],
   "source": [
    "model2.set_mode(0,1,0,mode='ns')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "b5b13363",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 500x400 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model2.plot()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
